A simple procedure for measuring surface convection heat transfer coefficients involves

coating the surface with a thin layer of material having a precise melting point temperature.

The surface is then heated and, by determining the time required for melting to occur, the

convection coefficient is determined. The following experimental arrangement uses the

procedure to determine the convection coefficient for gas flow normal to a surface.

Specifically, a long copper rod is encased in a super insulator of very low thermal

conductivity, and a very thin coating is applied to its exposed surface. If the rod is initially

at $25C$ and gas flow for which $h=200\frac{W}{m^2}K$ and $T_{}=300C$ is initiated, what is the

melting point temperature of the coating if melting is observed to occur at $t=400s?$